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Comparison of AUV Position Estimation Using Kalman Filter, Ensemble Kalman Filter and Fuzzy Kalman Filter Algorithm in the Specified Trajectories Ngatini, Ngatini; Apriliani, Erna; Nurhadi, Hendro
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 4, No 1 (2022)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v4i1.22912

This research explains a comparison estimation for AUV position using Kalman Filter (KF), Ensemble Kalman Filter (EnKF), and Fuzzy Kalman Filter (FKF) algorithm in some specified trajectories. Estimation is developed for AUV Segorogeni ITS which was built by the Institute Technology of Sepuluh Nopember (ITS), Indonesia. The specified trajectories are the diving, straight, and turning path which is the real trajectories. We compare the result estimation for each of the trajectories from the simulation and the RMSE (Root Mean Square Error). In this case, the best estimation is given by the difference estimation method. Fuzzy Kalman Filter gives the best result for the diving trajectory (Y-position and angle) and the straight trajectory. Ensemble Kalman Filter (EnKF) gives the best result for the X-position in the diving trajectory. While Kalman Filter gives the best result for the straight trajectory.Keywords: AUV; Kalman Filter (KF); Ensemble Kalman Filter (EnKF); Fuzzy Kalman Filter (FKF); AUV Segorogeni ITS. AbstrakPenelitian ini menjelaskan tentang perbandingan estimasi untuk posisi AUV antara algoritma Kalman Filter (KF), Ensemble Kalman Filter (EnKF) dan Fuzzy Kalman Filter (FKF) untuk trayektori tertentu. Estimasi dilakukan terhadap AUV Segorogeni ITS yang dibuat oleh ITS (Institut Teknologi Sepuluh Nopember), Indonesia. Trayektori yang diberikan adalah menyelam, lurus dan lintasan membelok yang merupakan lintasan real. Peneliti melakukan perbandingan untuk setiap lintasan berdasarkan hasil simulasi dan Root Mean Square Error (RMSE). Pada kasus ini estimasi terbaik diberikan oleh metode yang berbeda. Fuzzy Kalman Filter memberikan hasil terbaik untuk lintasan berbelok pada posisi-Y dan pada garis lurus. Ensemble Kalman Filter memberikan estimasi terbaik untuk posisi-X pada lintasan menyelam. Sedangkan Kalman Filter memberikan hasil terbaik untuk lintasan lurus.Kata kunci: AUV; Kalman Filter (KF); Ensemble Kalman Filter (EnKF); Fuzzy Kalman Filter (FKF); AUV Segorogeni ITS.

Comparison of AUV Position Estimation Using Kalman Filter, Ensemble Kalman Filter and Fuzzy Kalman Filter Algorithm in the Specified Trajectories Ngatini, Ngatini; Apriliani, Erna; Nurhadi, Hendro
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 4 No. 1 (2022)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v4i1.22912

This research explains a comparison estimation for AUV position using Kalman Filter (KF), Ensemble Kalman Filter (EnKF), and Fuzzy Kalman Filter (FKF) algorithm in some specified trajectories. Estimation is developed for AUV Segorogeni ITS which was built by the Institute Technology of Sepuluh Nopember (ITS), Indonesia. The specified trajectories are the diving, straight, and turning path which is the real trajectories. We compare the result estimation for each of the trajectories from the simulation and the RMSE (Root Mean Square Error). In this case, the best estimation is given by the difference estimation method. Fuzzy Kalman Filter gives the best result for the diving trajectory (Y-position and angle) and the straight trajectory. Ensemble Kalman Filter (EnKF) gives the best result for the X-position in the diving trajectory. While Kalman Filter gives the best result for the straight trajectory.Keywords: AUV; Kalman Filter (KF); Ensemble Kalman Filter (EnKF); Fuzzy Kalman Filter (FKF); AUV Segorogeni ITS. AbstrakPenelitian ini menjelaskan tentang perbandingan estimasi untuk posisi AUV antara algoritma Kalman Filter (KF), Ensemble Kalman Filter (EnKF) dan Fuzzy Kalman Filter (FKF) untuk trayektori tertentu. Estimasi dilakukan terhadap AUV Segorogeni ITS yang dibuat oleh ITS (Institut Teknologi Sepuluh Nopember), Indonesia. Trayektori yang diberikan adalah menyelam, lurus dan lintasan membelok yang merupakan lintasan real. Peneliti melakukan perbandingan untuk setiap lintasan berdasarkan hasil simulasi dan Root Mean Square Error (RMSE). Pada kasus ini estimasi terbaik diberikan oleh metode yang berbeda. Fuzzy Kalman Filter memberikan hasil terbaik untuk lintasan berbelok pada posisi-Y dan pada garis lurus. Ensemble Kalman Filter memberikan estimasi terbaik untuk posisi-X pada lintasan menyelam. Sedangkan Kalman Filter memberikan hasil terbaik untuk lintasan lurus.Kata kunci: AUV; Kalman Filter (KF); Ensemble Kalman Filter (EnKF); Fuzzy Kalman Filter (FKF); AUV Segorogeni ITS.

Auto Floodgate Control Using EnKf-NMPC Method Evita Purnaningrum; Erna Apriliani
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 2 No. 1 (2016)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

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One of the flood controls, especially in the downstream areas are barrage. Those are optimized using Ensemble Kalman filter based non linear predictive control. Ensemble Kalman Filter is used to predict water levels and flow of waters when it reaches the barrage. The results obtained from this method is then used as input for controlling the floodgates. Simulations are performed in three circumstances, namely the normal flow, flooding and drought. For normal flow, using optimum quantities are obtained from NMPC by opening the floodgates. Simulations were performed for 100 hours, with a gap of 5 per hour of observation. EnKf fulfilled with RMSE yields accuracy of the system and estimates of less than 1, RMSE debit is 0.5346 and RMSE water level is 0.2716. Furthermore the operation of the opening gate achieves optimum value, with the movement of between 40 - 65 per cent, with an average difference of movement is 0.10065 percent. Flood conditions, the water flow 2.000 m3/s and the water level 10 m operation of opening gate ranging between 98 - 100 per cent and the amount of the difference opening gate is 0.028835. RMSE to estimate the flow rate of 1.5835, while for the water level of 0.3145. While the flow conditions dry, with water flow 10 m3/s and the water level 1 m operation of opening gate ranging between 0 - 1 percent and the amount of the difference opening gate is 0.41289 percent. RMSE to estimate the flow rate of 0.0826, while for the water level of 0.0677.

Effect of Major Axis Length to the Pressure on Ellips Chairul Imron; Erna Apriliani
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 2 No. 3 (2016)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

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Fluid concept has been widely applied to solve problems of daily life, one example is the problem of fluid flow around an elliptical cylinder. We have a goal to solve the problem of fluid flow through three cylindrical ellipses using side-by-side configuration. The equation we use to solve the problem is the Navier-Stokes equations, incompressible, viscous and unsteady. We use the finite difference method with a uniform grid and SIMPLE (Semi Implicit Method for Pressure-Linked Equations) algorithms. Results of this study were used to obtain the amount of pressure that is received by an ellipse in the middle and to construct mathematical models. The profile of the fluid flow is simulated by varying the length of the major axis of the ellipse in the middle where K/5a = 1.0; 1.1; 1.2; 1.3; 1.4 and 1.5 and Reynolds Re = 3.000 and the distance between the ellipse is 3.

Convergence and Completeness in L_2 (P) with respect to a Partial Metric Annisa Rahmita Soemarsono; Mahmud Yunus; Erna Apriliani; Adam Adam
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 9 No. 1 (2023)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

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Metric spaces can be generalized to be partial metric spaces. Partial metric spaces have a unique concept related to a distance. In usual case, there is no distance from two same points. But, we can obtain the distance from two same points in partial metric spaces. It means that the distance is not absolutely zero. Using the basic concept of partial metric spaces, we find analogy between metric spaces and partial metric spaces. We define a metric d^p formed by a partial metric p, with applying characteristics of metric and partial metric. At the beginning, we implement the metric d^p to determine sequences in L_2 (P). We then ensure the convergence and completeness in L_2 [a,b] can be established in L_2 (P). In this study, we conclude that the convergence and completeness in L_2 [a,b] can be established in L_2 (P) by constructing a partial metric p_2 induced by a metric d^p.

KAJIAN ANALISIS DALAM METODE ASIMILASI DATA Erna Apriliani
Limits: Journal of Mathematics and Its Applications Vol. 6 No. 1 (2009): Limits: Journal of Mathematics and Its Applications Volume 6 Nomor 1 Edisi Mei
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Asimilasi data adalah suatu metode estimasi yang diperoleh dari penggabungan antara model sistem dan data-data pengukuran. Salah satu metode asimilasi data adalah Kalman lter yang merupakan metode estimasi variabel keadaan dari sistem dinamik stokastik. Filter Kalman telah banyak diterapkan pada berbagai bidang ilmu antara lain hidrodinamika, meteorologi, navigasi pesawat dan masalah matematika nansial. Algoritma dasar dari Filter Kalman telah banyak mengalami perkembangan agar dapat diterapkan pada masalah real dan mempunyai waktu komputasi yang cepat. Pada makalah ini akan disajikan beberapa contoh pengembangan algoritma lter Kalman atau asimilasi data secara umum yang memerlukan kajian analisis. Aspek-aspek analisis yang sering diperlukan antara lain norm matriks, konvergensi dan kestabilan.

Prediksi Penyebaran Covid-19 di Indonesia dan Jawa Timur dengan Metode Extended Kalman Filter Helisyah Nur Fadhilah; Erna Apriliani; Didik Khusnul Arif
Limits: Journal of Mathematics and Its Applications Vol. 18 No. 1 (2021): Limits: Journal of Mathematics and Its Applications Volume 18 Nomor 1 Edisi Me
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Saat ini pandemi Covid-19 telah menyebar ke seluruh dunia, tidak terkecuali Indonesia. Dalam pemodelan matematika, penyebaran Covid-19 dapat digambarkan melalui model matematika epidemiologi SIRD ( Susceptible, Infected, Recover, Death ). Pertama model non-linier SIRD didiskritkan dan selanjutnya dilakukan prediksi puncak penyebaran Covid-19 dengan menggunakan metode Extended Kalman Filter (EKF). Dengan data aktual Infected, Recover, dan Death yang merupakan data harian, modifikasi EKF dapat memprediksi puncak infeksi Covid-19 untuk satu bulan kedepan. Simulasi dilakukan dengan 3 macam pembatasan pergerakkan pada masyarakat yaitu : tanpa adanya pembatasan (100%), 75%, dan 50% pergerakkan. Hasil prediksi dengan modifikasi EKF menunjukkan dengan dilakukan pembatasan pergerakkan 50% pada masyarakat di Indonesia dan Jawa Timur dapat mempercepat terjadinya puncak infeksi dengan jumlah individu terinfeksi lebih sedikit

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